Functional Regression Models for Epistasis Analysis of Multiple Quantitative Traits

To date, most genetic analyses of phenotypes have focused on analyzing single traits or analyzing each phenotype independently. However, joint epistasis analysis of multiple complementary traits will increase statistical power and improve our understanding of the complicated genetic structure of the complex diseases. Despite their importance in uncovering the genetic structure of complex traits, the statistical methods for identifying epistasis in multiple phenotypes remains fundamentally unexplored. To fill this gap, we formulate a test for interaction between two genes in multiple quantitative trait analysis as a multiple functional regression (MFRG) in which the genotype functions (genetic variant profiles) are defined as a function of the genomic position of the genetic variants. We use large-scale simulations to calculate Type I error rates for testing interaction between two genes with multiple phenotypes and to compare the power with multivariate pairwise interaction analysis and single trait interaction analysis by a single variate functional regression model. To further evaluate performance, the MFRG for epistasis analysis is applied to five phenotypes of exome sequence data from the NHLBI’s Exome Sequencing Project (ESP) to detect pleiotropic epistasis. A total of 267 pairs of genes that formed a genetic interaction network showed significant evidence of epistasis influencing five traits. The results demonstrate that the joint interaction analysis of multiple phenotypes has a much higher power to detect interaction than the interaction analysis of a single trait and may open a new direction to fully uncovering the genetic structure of multiple phenotypes.Author Summary: The widely used statistical methods test interaction for single phenotype. However, we often observe pleotropic genetic interaction effects. The simultaneous gene-gene (GxG) interaction analysis of multiple complementary traits will increase statistical power to detect GxG interactions. Although GxG interactions play an important role in uncovering the genetic structure of complex traits, the statistical methods for detecting GxG interactions in multiple phenotypes remains less developed owing to its potential complexity. Therefore, we extend functional regression model from single variate to multivariate for simultaneous GxG interaction analysis of multiple correlated phenotypes. Large-scale simulations are conducted to evaluate Type I error rates for testing interaction between two genes with multiple phenotypes and to compare power with traditional multivariate pair-wise interaction analysis and single trait interaction analysis by a single variate functional regression model. To further evaluate performance, the MFRG for interaction analysis is applied to five phenotypes of exome sequence data from the NHLBI’s Exome Sequencing Project (ESP) to detect pleiotropic GxG interactions. 267 pairs of genes that formed a genetic interaction network showed significant evidence of interactions influencing five traits.